Hi,
I have the equation:
The auxiliary equation has the solutions
So the general solution would look like this
Now, let
gives
Can be simplified down to
This is where i am stuck, how do you combine this with the general solution?
//Thanks
Hi,
I have the equation:
The auxiliary equation has the solutions
So the general solution would look like this
Now, let
gives
Can be simplified down to
This is where i am stuck, how do you combine this with the general solution?
//Thanks
Well, you know that since there are no terms, and since there is exactly one term.
As a sidebar, it's easier to answer things like this clearly when you use standard notations. Your initial equation indicates as the independent variable, and is what is typically used for calculating the characteristic equations.
Just add it to the general solution of the homogeneous equation!
If L(y) is a linear differential operator, then L(y+ y2)= L(y1)+ L(y2). If yh satifies L(yh)= 0 and yp satisfies L(yp)= f(x), then L(yh+ yp)= L(yh)+ L(yp)= 0+ f(x)= f(x). Further, if y is any solution to L(y)= f(x), then L(y- yp)= L(y)- L(yp)= f(x)- f(x)= 0 so that y- yp= yh, a solution to the homogeneous equation. The general solution to the entire equation is the the general solution to the homogeneous equation plus any solution to the entire equation. That's the whole point of this method!